Preface

Acknowledgments

1 Introduction

References

2 Matrices over Field F（z） of Rational Functions in Multi-parameters

2.1 Polynomials over Field F（z） or Ring F（z）[隴

2.2 Operations and Determinant of Matrix over F（z）

2.3 Elementary Operations of Matrices over F（z） and Some Conclusions

2.4 Operation and Canonical Form of Matrix over F（z）

2.4.1 Matrix over F（z） and its canonical expression

2.4.2 Characteristic matrix

2.4.3 Two canonical forms of nonderogatory matrix

2.4.4 Rational canonical form and general Jordan canonical form

2.5 Reducibility of Square Matrix over F（z）

2.6 Reducibility Condition of Class of Matrices over F（z）

2.6.1 A class of RFM

2.6.2 Some lemmas and definitions

2.6.3 Reducibility condition

2.6.4 Applications

2.6.5 Summary

2.7 Two Properties

2.7.1 Some lemmas

2.7.2 Type-l matrix has two properties

2.7.3 Problems

2.8 Independent Parameters and a Class oflrreducible Polynomials over F（z） [隴

2.9 Conclusions

2.10 New Model and Its Reducibility

2.10.1 The new model

2.10.2 Reducibility condition

References

3 Controllability and Observability of Linear Systems over F（z）

3.1 Controllability and Observability in Time Domain

3.1.1 Preliminaries [Lu， 2001]

3.1.2 Controllability criteria [Lu， 2001]

3.1.3 The canonical decomposition of controllability and observability of systems

3.1.4 Criterions to linear physical systems

3.1.5 Applications to control systems

3.2 Controllability and Observability in Frequency Domain

3.2.1 General systems [Lu et al.， 1991]

3.2.2 SC-SO of composite systems [Lu et al.， 1991]

3.2.3 Polynomial matrix [Liu， 2008] References

4 Electrical Networks over F（z）

4.1 Resistor-Source Networks over F（z）

4.1.1 Introduction

4.1.2 General resistor-source networks

4.1.3 Unhinged networks

4.1.4 Effects of single source

4.2 Separability and Reducibility Conditions of RLC Networks over F（z） and Their Applications

4.2.1 Introduction

4.2.2 Preliminaries

4.2.3 Separability condition

4.2.4 Separability and reducibility

4.2.5 Applications

4.3 Controllability and Observability of RLC Networksover F（z）

5 Further Thought

Appendix

Index

由鲁凯生编著者的《多元有理函数系统与电网络（英文版）》主要介绍多元有理函数系统与电网络的结构和性质，详细讨论了域F（z）上的矩阵及其特征多项式的可约性条件；定义了I型矩阵并证明了它的两个基本性质；介绍了独立参量的变量代换条件，域F（z）上线性系统的结构能控能观性问题、电网络的结构性质、RLCM网络的可断性和可约性及能控能观性、有源网络状态方程的存在性条件、能控能观性条件等；附录给出了《多元有理函数系统与电网络（英文版）》用到的一些知识。

　　《多元有理函数系统与电网络（英文版）》适合电子电气、自动化和应用数学（矩阵理论）专业的研究生、科研和工程技术人员参考阅读。